TS EAMCET · Maths · Differentiation
If \(y=\log \left[\tan \sqrt{\frac{2^x-1}{2^x+1}}\right], x\gt0\), then \(\left(\frac{d y}{d x}\right)_{x=1}=\)
- A \(\frac{4 \sqrt{2} \log 2}{9 \sin \left(\frac{2}{\sqrt{3}}\right)}\)
- B \(\frac{4 \sqrt{3} \log 2}{9 \sin \left(\frac{\sqrt{3}}{2}\right)}\)
- C \(\frac{4 \sqrt{3} \log 2}{9 \sin \left(\frac{2}{\sqrt{3}}\right)}\)
- D \(\frac{4 \sqrt{2} \log 2}{9 \sin \left(\frac{\sqrt{3}}{2}\right)}\)
Answer & Solution
Correct Answer
(C) \(\frac{4 \sqrt{3} \log 2}{9 \sin \left(\frac{2}{\sqrt{3}}\right)}\)
Step-by-step Solution
Detailed explanation
\(y=\log \left[\tan \sqrt{\frac{2^x-1}{2^x+1}}\right] \Rightarrow e^y=\tan \sqrt{\frac{2^x-1}{2^x+1}}\)....(i) Let \(\frac{2^x-1}{2^x+1}=v \Rightarrow v_{x=1}=\frac{1}{3}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The differential equation of the family of circles with fixed radius units and centre on the line , isTS EAMCET 2022 Medium
- If \(\alpha, \beta, \gamma\) are the roots of \(x^3-3 x^2-4 x+12=0\), then \(\sum(\alpha+\beta)^2\) is equal toTS EAMCET 2021 Easy
- If the line joining the points \(A(1,0,0)\) and \(B(0,0,1)\) is a normal to the plane \(\pi\) which passes through the point \(A\), then the angle between the planes \(\pi\) and \(x+y+z=6\) isTS EAMCET 2018 Medium
- If \(\sec \left(\log _2 y^2\right)=\operatorname{cosec}\left(\log _2 x^2\right)\), then \(\frac{d y}{d x}=\)TS EAMCET 2023 Hard
- For \(h, k \in N\), let \(\mathrm{P}(h, k)\) be the point of intersection of the curves \(x^2 y-x^3=8\) and \(y^3-x y^2=32\). If \(\theta\) is the acute angle between these two curves at \(P, \operatorname{then} \tan \theta=\)TS EAMCET 2023 Easy
- If \(n\) is a positive integer, then \((1+i)^n \div(1-i)^n=-i\), then \(n\) will be of the formTS EAMCET 2021 Easy
More PYQs from TS EAMCET
- At a certain place, the angle of dip is \(60^{\circ}\) and the horizontal component of the earth's magnetic field \(\left(B_H\right)\) is \(0.8 \times 10^{-4} \mathrm{~T}\). The earth's overall magnetic field isTS EAMCET 2014 Medium
- If the value of \(\sqrt{-5-12 i}+\sqrt{7+24 i}\) is a negative real number \(k\), then \(k=\)TS EAMCET 2023 Medium
- The work function of a photosensitive metal surface is 1.1 eV . Two light beams of energies 1.5 eV and 2 eV incident on the metal surface. The ratio of the maximum velocities of the emitted photoelectrons isTS EAMCET 2024 Medium
- Let \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be the functions defined by \(f(x)=\frac{x}{1+x^2}\), \(x \in R, g(x)=\frac{x^2}{1+x^2}, x \in R\) Then, the correct statement (s) among the following is/are : (a) both \(f . g\) are one-one (b) both \(f . g\) are onto (c) both \(f . g\) are not one-one as well as not onto (d) \(f\) and \(g\) are onto but not one-oneTS EAMCET 2019 Easy
- What is the equivalent weight of methanol if one mole of is combusted to form and :TS EAMCET 2019 Medium
- A plane \(\Pi\) is passing through the points \(A=(0,0,2), B=(1,0,1)\) and \(C=(\beta, 1,1)\). If the plane \(\Pi\) makes angle \(\alpha\) and \(\beta\) with the \(X Y\) and \(X Z\)-coordinate planes respectively, then \(\sin ^2 \alpha+\sin ^2 \beta=\)TS EAMCET 2020 Medium